Cubic Spline Solution of linear fourteenth order boundary value problems

Abstract

As higher order differential equations have constantly been tiresome and problematic to resolve for the mathematicians and engineers so diverse numerical procedures were conceded out to acquire numerical estimates to such problems. In this paper an innovative numerical procedure is developed to estimate the fourteenth-order boundary value problems (BVPs) using Polynomial and Non-Polynomial Cubic spline. The procedures adopted in our work are based on cubic polynomial and non-polynomial spline method together with the decomposition procedure. In this paper polynomial and non-polynomial cubic splines along with the finite difference approximations will be used to squeeze the system of second order Boundary Value Problems in such a way that it will be converted into to a system consists of linear algebraic equations along with boundary conditions. These strategies will be operated on two problems to evidence the handiness of the technique by means of step size h = 1/5. The exactness of this method for detailed investigation is equated with the precise solution and conveyed through tables.

Keywords

• fourteenth order, numerical solution, central finite difference approximations, non-polynomial spline, system of linear algebraic equations, polynomial spline